The Elements of Solid Geometry: With Numerous Exercises |
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The Elements of Solid Geometry. With Numerous Exercises Arthur Latham Baker No preview available - 2017 |
Common terms and phrases
ABCD altitude Analysis angles are equal B₁ B₂ base edge bisect called centre cone cylinder cone of revolution conic section Construction convex cube curve cutting plane diagonals diameter dicular dihedral angles directrix distance ellipse equally distant equilateral equivalent face angles feet Find the height Find the volume focus frustum given line given point Hence homologous lines hyperbola inscribed intersection isosceles lateral area lateral edges lateral faces lune M₁ mid-section Notation parabola parallel planes perpen plane angle pole polyhedral angle prism cylinder prismatoid Proof pyramid cone pyramid whose base radii radius ratio rectangular parallelopiped regular pentagon regular polyhedron regular pyramid revolving right angles right circular cone right prism Scholium segment sides slant height sphere spherical angle spherical degrees spherical excess spherical polygon spherical surface spherical triangle straight line symmetrical tangent THEOREM total surface triangular pyramid trihedral upper base vertex vertices
Popular passages
Page 91 - The area of the surface generated by a straight line revolving about an axis in its plane is equal to the product of the projection of the line on the axis by the circumference whose radius is a perpendicular erected at the middle point of the line and terminated by the axis.
Page 71 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within, called the centre. A sphere may be
Page xii - A straight line is perpendicular to a plane when it is perpendicular to every straight line of the plane which passes through its foot, that is, the point where it meets the plane. Conversely, the plane is perpendicular to the line.
Page xi - 1. A plane is a surface such that a straight line joining any two points in it lies wholly in the surface. A plane is indefinite in extent, so that however far the straight line is produced, all its points lie in the plane ; but
Page 88 - A zone is the portion of the surface of a sphere included between two parallel planes. The circumferences of the sections made by the planes, are called the bases of the zone, and the distance between the planes is its altitude.
Page 82 - The arc, of a great circle drawn from the vertex of an isosceles triangle to the middle of the base, bisects the vertical angle, is perpendicular to the base, and divides the triangle into two symmetrical triangles. PROPOSITION
Page 71 - A diameter of a sphere is a straight line passing through the centre and limited by the surface. Since all the radii of a sphere are equal, and a diameter is equal to two radii, all the diameters of a sphere are equal.
Page 77 - A point on the surface, of a sphere, which is at the distance of a quadrant from each of two other points, not the extremities of a diameter, is a pole of the great circle passing through these points.
Page 3 - foot of a, perpendicular to a plane a straight line is drawn at right angles to any line in the plane, and its intersection with that line is joined to any point of the perpendicular, this last line will
Page 57 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism and whose vertices are the three vertices of the upper base.